In a jazz walking bassline it is perfectly acceptable to play another chord tone on the first beat of a bar. The third can work particularly well and still very much helps to outline the chord progression. In places where chords only last two beats it can sometimes be smoother to connect them with non-root notes.You should hit the root at the first beat. That's what the bass is for.
Or do it on beat three. To my ear a jazz walking line often sounds best with the chord tones (including the root) on beats one and three, and with other connecting notes on beats two and four. Also if you were playing a descending line that took you to the third on beat one then it would be natural to keep descending and reach the root on beat three.If you skip the root on beat one, do it on beat two.
Remember also that whether any particular note works on a given beat depends on the notes that came before it and the notes that follow, so the same note that did work in a certain bar last chorus might sound weird on the same beat of that bar next chorus if you approach it a different way.
In any case there are plenty of exceptions to any of these sorts of rules. Better to think of them as guidelines than rules.